Producing Huge Spin Alignment in Inelastic Excitations of ...

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t 7 Li 7 Li t beam-axis we Can reconst momentum back together Producing Huge Spin Alignment in Inelastic Excitations of Clustered Nuclei D. E. M. Hoff, K.W. Brown, R.J. Charity, J.M. Elson, C.D. Pruitt, L.G. Sobotka, T. B. Webb [WU-StL] G. Potel [NSCL/FRIB] A. Saastamoinen, B. Roeder and the MARS group [TAMU] In most nuclear reactions (fusion, quasi-elastic and deeply inelastic scattering) the total angular momentum is dominated by the large reservoir contained in orbital motion. It is not surprising, then, that the exit channel fragments tend to acquire an aligned spin perpendicular to the beam-axis. After analyzing a previous experiment with 7 Be at MSU a huge spin alignment (~50%!) parallel to the beam-axis was found for inelastically excited 7 Be*[1]. We performed an analogous experiment at TAMU using 7 Li which also displayed a large longitudinal spin alignment. In particular we studied the reactions: and observed a large spin-alignment parallel to the beam-axis in all cases. Experimental Methods and Results The experiment was conducted in the MARS beam line at Texas A&M in August 2015. The K500 was used to provide a primary 24 MeV/A 7 Li beam. We used two Si-CsI(Tl) telescopes mounted on a rail system. One telescope array was placed at 15 cm from the target and the other at 35 cm. This dual-annular telescope system provided nearly complete azimuthal coverage and polar angular coverage of 1.8 o to 16 o , with a small gap at 5.7 o . Beam Axis L’ L Beam Axis Beam Axis ˆ z 7 Li ground state is well described as an + t with l = 1 internal orbital motion, and the J = 7/2 - state with l = 3. The inelastic excitation is almost exclusively a quadrupole transition and the reaction “spins up” 7 Li along the beam-axis (i.e. +3/2 +7/2, -3/2 -7/2). The large beam energy and small excitation energy forces the reaction plane to tilt (L = 0, M = ± 2) because of angular momentum and excitation energy matching. Additional findings suggest coherent L-wave mixing washes out the oscillations of alignment in angle expected for a single L-wave. References: [1] R.J. Charity et al., PRC 91, 024610 (2015) 7 Li Level Scheme 12 C Level Scheme 7 Li Excitation Reconstruction 12 C Excitation Reconstruction Invariant Mass (from +t) Spectrum Extracted Target Excitation (from 2-body kinematics) If reaction product’s spin is aligned perpendicular to the beam axis fragments from its decay will be preferentially emitted in a plane containing the beam-axis (cos() = ±1). This is not observed. If the reaction product’s spin is aligned parallel to the beam axis fragments from he decay will be preferentially emitted in the x-y plane (cos() = 0). This is observed. Standard theory of angular correlations says the distribution will be dictated by Legendre Polynomials weighted by the outgoing magnetic substate density matrix. In the inelastic excitation studied here (conducted at intermediate energy) the produced 7 Li* fragments are highly aligned parallel the beam axis. R r r αC r tC 12 C α t θ Density Matrix Fit Legendre Polynomial contributions We reconstruct events by adding momentum back together. The reaction code FRESCO, exercised with a three-body (cluster) model, was able to reproduce the alignment (black = data) and its angular distribution. To understand the physics that generates the longitudinal alignment, a dissectible 3- body reaction code was written. 3/2 1/2 -1/2 -3/2 3/2 -7/2 -5/2 -3/2 -1/2 1/2 5/2 7/2 3/2 1/2 -1/2 -3/2 3/2 -7/2 -5/2 -3/2 -1/2 1/2 5/2 7/2 3/2 1/2 -1/2 -3/2 3/2 -7/2 -5/2 -3/2 -1/2 1/2 5/2 7/2 12 C p in p out R Full FRESCO Calculation of T-Matrix CG for initial spin projection to final spin projection via K = 2 quadrupole transition huge “spin-up”. Increased J of the projectile cannot come from longitudinal reduction in linear momentum. Reaction plane must tilt. Δp = ΔL R = s E CM 2μ - s E CM - Ex 2μ h3/2,m i ; 2,M | 7/2,m f i 2 CG for K = 2 change in the orientation of the reaction orbital angular momentum for one L-wave, near the grazing value of L g = 35. × h3/2,m i ; 2,M | 7/2,m f i 2 h35, 0; 2,M | 35,M i 2 The entrance and exit L-waves are the same but the projection has changed, i.e. the reaction plane has tilted. M = m f - m i Angular Correlations for 5-15 deg. in CM frame = Introduction Measuring Alignment Cluster Model Calculations Alignment Mechanism Conclusion m* 4 3 2 1 0 1 2 3 4 s* m*,m* ρ 0 0.05 0.1 0.15 0.2 0.25 0.3 Diagonal elements of FRESCO generated density matrix. [Counts] [Counts] Ex [MeV] [Counts] Ex [MeV] m i m i m i m f m f m f 7 Li(J =3/2 - )+ Be/C/Al ! 7 Li (J =7/2 - )+ Be/C/Al (all remaining in GS) s* m*,m* ρ |T m i ,m f | 2 ⇡hJ i ,m i ; K,M | J f ,m f i 2 hL g , 0; K,M | L g ,M i 2

Transcript of Producing Huge Spin Alignment in Inelastic Excitations of ...

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� Many parameter fit (16) of fragment’s angular distribution extracts the magnetic sub-state distribution (see PRC 91 024610 for more details)

� Spin alignment along the beam axis produces more transverse events i.e. projectile fragments found perpendicular to beam axis (ψ = 90 degrees)

� Spin alignment perpendicular to the beam axis produces more longitudinalevents i.e. fragments found along beam axis (ψ = 0,180 degrees)

t

𝛼

7Li

7Li

t

Experimental Methods

𝛼

beam-axis

beam-axis

Invariant Mass Method

From Special Relativity:

� Rest mass is invariantto the reference frame.

� Excited nuclei have more energy so their rest

mass is increased (just like excited atoms)

� By measuring total Energy and Momentum we

also measure the invariantmass showing us

excited states of the nuclei.

Can reconstruct events by adding

momentum back together

Producing Huge Spin Alignment in Inelastic Excitations of Clustered Nuclei

D. E. M. Hoff, K.W. Brown, R.J. Charity, J.M. Elson, C.D. Pruitt, L.G. Sobotka, T. B. Webb [WU-StL]G. Potel [NSCL/FRIB]

A. Saastamoinen, B. Roeder and the MARS group [TAMU]

In most nuclear reactions (fusion, quasi-elastic and deeply inelastic scattering) the total angular momentum is dominated by the large reservoir contained in orbital motion. It is not surprising, then, that the exit channel fragments tend to acquire an aligned spin perpendicular to the beam-axis.

After analyzing a previous experiment with 7Be at MSU a huge spin alignment (~50%!) parallel to the beam-axis was found for inelastically excited 7Be*[1].

We performed an analogous experiment at TAMU using 7Li which also displayed a large longitudinal spin alignment. In particular we studied the reactions:

and observed a large spin-alignment parallel to the beam-axis in all cases.

Experimental Methods and ResultsThe experiment was conducted in the MARS beam line at Texas A&M in August 2015. The K500 was used to provide a primary 24 MeV/A 7Li beam.

We used two Si-CsI(Tl) telescopes mounted on a rail system. One telescope array was placed at 15 cm from the target and the other at 35 cm.

This dual-annular telescope system provided nearly complete azimuthal coverage and polar angular coverage of 1.8o to 16o, with a small gap at 5.7o.

Outline� Introduction

� Molecular Alignment� Experimental Methods

� Si-CsI telescope “stack”� Data Acquisition � PID (Particle Identification)� Experiment Setup� Invariant Mass Method

� Monte Carlo Simulations� Preliminary Data

� Sources of Systematic Error

Beam Axis

L’L

Beam Axis

Beam Axisz

7Li ground state is well described as an 𝛼 + t with l = 1 internal orbital motion, and the J𝜋 = 7/2- state with l = 3. The inelastic excitation is almost exclusively a quadrupole transition and the reaction “spins up” 7Li along the beam-axis (i.e. +3/2 → +7/2, -3/2 → -7/2).

The large beam energy and small excitation energy forces the reaction plane to tilt (∆L = 0, M = ± 2) because of angular momentum and excitation energy matching.

Additional findings suggest coherent L-wave mixing washes out the oscillations of alignment in angle expected for a single L-wave.

References: [1] R.J. Charity et al., PRC 91, 024610 (2015)

7Li Level Scheme

12C Level Scheme

7Li Excitation Reconstruction

12C Excitation Reconstruction

Invariant Mass (from 𝛼+t) Spectrum ➡

Extracted Target Excitation (from 2-body kinematics)

If reaction product’s spin is aligned perpendicular to the beam axis fragments from its decay will be preferentially emitted in a plane containing the beam-axis (cos(𝜓) = ±1). This is not observed.

If the reaction product’s spin is aligned parallel to the beam axis fragments from he decay will be preferentially emitted in the x-y plane (cos(𝜓) = 0). This is observed.

Standard theory of angular correlations says the distribution will be dictated by Legendre Polynomials weighted by the outgoing magnetic substate density matrix. In the inelastic excitation studied here (conducted at intermediate energy) the produced 7Li* fragments are highly aligned parallel the beam axis.

Rr

rαC

rtC

12C

α

t

θ

Figure 1: Coordinates used for the description of the 7Li–12C collision in a three–body model.

In first order in the coupling �, the amplitude Tmi,m f is

Tmi,m f =

Z�(�)⇤

1 (R)�⇤1,m f(r)�(R, r↵C , rtC)�(+)

0 (R)�0,mi(r) dr dR. (7)

In order to do the partial wave decomposition, we write

�(+)0 (R; ki) =

4⇡kiR

X

la

ilaei�lai fla(R)

p2la + 1

hYla(R)Yla(ki)

i00, (8)

�(�)⇤1 (R; k f ) =

4⇡k f R

X

lb

i�lbei�lbf glb(R)

p2lb + 1

hYlb(R)Ylb(k f )

i00, (9)

�0,mi(r) = u0(r)Ylimi(r); �1,m f (r) = u1(r)Yl f

m f (r). (10)

In our case, li = 1, l f = 3, and ki,k f are the initial and final momenta respectively.The functions fla(R) and glb(R) are the solutions of the radial Schrodinger equa-tion in the initial and final channel respectively, and �la

i ,�lbf are the corresponding

Coulomb phase shifts. Then,

Tmi,m f =16⇡2

kik f

X

lalb

ila�lbei(�lai +�

lbi )p

2la + 1p

2lb + 1 (�1)m f

⇥Z

fla(R) glb(R)R2 u0(r) u1(r)Yli

mi(r)Yli�m f

(r)hYla(R)Yla(ki)

i00

⇥hYlb(R)Ylb(k f )

i00�(R, r↵C , rtC) dr dR, (11)

2

Density Matrix Fit

Legendre Polynomial contributions

We reconstruct events byadding momentum back

together.

The reaction code FRESCO, exercised with a three-body (cluster) model, was able to reproduce the alignment (black = data) and its angular distribution.

To understand the physics that generates the longitudinal alignment, a dissectible 3-body reaction code was written.

3/21/2

-1/2-3/2

3/2-7/2 -5/2 -3/2 -1/2 1/2 5/2 7/2

3/21/2

-1/2-3/2

3/2-7/2 -5/2 -3/2 -1/2 1/2 5/2 7/2

3/21/2

-1/2-3/2

3/2-7/2 -5/2 -3/2 -1/2 1/2 5/2 7/2

12C

pin pout

R

Full FRESCO Calculation of T-Matrix

CG for initial spin projection to final spin projection via K = 2

quadrupole transition ➡ huge “spin-up”.

Increased J of the projectile cannot come from longitudinal reduction in linear momentum. Reaction plane must tilt.

�p =�L

R

=

sECM

2µ�

sECM �Ex

h3/2,mi ; 2,M | 7/2,mf i2

CG for K = 2 change in the orientation of the reaction orbital

angular momentum for one L-wave, near the grazing value of Lg = 35.

×

h3/2,mi ; 2,M | 7/2,mf i2 h35, 0 ; 2,M | 35,Mi2

The entrance and exit L-waves are the same but the projection has changed, i.e. the

reaction plane has tilted.

M = mf �mi

Angular Correlations for 5-15 deg. in CM frame

➡ =

Introduction

Measuring Alignment Cluster Model Calculations

Alignment Mechanism Conclusion

m*4− 3− 2− 1− 0 1 2 3 4

s* m*,m

0

0.05

0.1

0.15

0.2

0.25

0.3

Diagonal elements of FRESCO generated density matrix.

[Cou

nts]

[Counts]

Ex [M

eV]

[Counts]

Ex [M

eV]

mimi mi

mf mf mf

7Li(J⇡ = 3/2�) +Be/C/Al ! 7Li⇤(J⇡ = 7/2�) +Be/C/Al (all remaining in GS)

m*4− 3− 2− 1− 0 1 2 3 4

s* m*,m

0

0.05

0.1

0.15

0.2

0.25

0.3

|Tmi,mf |2 ⇡ hJi,mi ; K,M | Jf ,mf i2 hLg, 0 ; K,M |Lg,Mi2